200 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



causes a peculiar irregularity in the ray diagram, as 

 shown in Figure 6; in this figure rays are drawn for 

 initial inclinations in 0.1° steps from 1.0° to 2.5°. 

 Rays whose vertices lie below 48 ft (1.0°, 1.1°, 1.2°) 

 are bent downward strongly by the strong negative 

 gradient below the knee. Rays rising above 48 ft 

 (1.3°, 1.4°, etc.), however, are bent downward only 

 weakly by the weak negative gradient above the 

 knee, and diverge more rapidly; their divergence is 



400 800 1200 1600 2000 2400 2600 

 RANGE IN YARDS 



Figure 5. Observed and calcuia*^ed variation of peak 

 pressure with range for a negative temperature gradi- 

 ent. Hydrophone depth, 54 ft; lap depth, 100 ft; 

 sound conditions as shown in Figure 6. 



further increased when they curve back down through 

 the knee. The result of this "double layer effect" is a 

 "hole" in the sound field immediately beyond the 

 1.2-degree ray, i.e., as a sharp dip in the intensity- 

 range curve, as shown in Figure 5. The theoretical 

 curve for this figure was not fitted to the points, but 

 was computed from the known absolute strength of 

 the source. At its minimum this theoretical intensity 

 is some 14 db lower than that which would be pre- 

 dicted by the inverse square law, and it is therefore 

 quite significant that the observed intensities follow 

 it so closely. As the shadow boundary is approached 

 the observed intensities drop markedly before the 

 computed shadow boundary is reached. This might 

 be due to a departure from ray theory or to a slight 

 error in the assumed temperature distribution near 

 the surface which would cause the computed shadow 

 boundary to be too far out. While data on the time 

 of rise of the pressure to its peak value (see Table 2 



on page 204) favor the latter interpretation, the sys- 

 tematic tendency of the observed shadow boundary 

 to lie closer than predicted, discussed in Section 5.4.1, 

 suggests that some other cause must be found for 

 this apparent discrepancy. 



9.2.3 Shadow Zones and DiiFraction 



As we have seen in Figures 3, 4, and 5 of Section 

 9.2.2, signals of appreciable intensity are received in 

 places where no rays on the sound ray diagram 

 penetrate. This phenomenon is familiar in experi- 

 ments with sinusoidal sound and has been discussed 

 in Section 5.4. This and other departures of observed 

 intensities and pulse forms from those computed by 

 applying ray theory to bathythermograph observa- 

 tions may be due to any of several causes. In the first 

 place, the concept of propagation of sound along ray 

 paths is only approximate; a more exact application 

 of acoustical theory predicts that some sound should 

 penetrate into the shadow zone by diffraction, and 

 that in and near the shadow zone the shape of the 

 pulse should be somewhat different from its shape 

 close to the source. In the second place, it is known 

 that the temperature in surface layers of the ocean 

 is not simply a function of the depth, but varies ap- 

 preciably from one position to another in the same 

 horizontal plane. Thus a set of rays which were really 

 accurately constructed would differ in many features 

 from the rays which one computes from the assump- 

 tion that temperature is a function of depth alone. 

 Thirdly, the water is not homogeneous but contains 

 bubbles, fish, etc., which can scatter sound and cause 

 its velocity to vary with the frequency. Finally, the 

 water is not at rest; portions of it may be set in 

 motion relative to the rest by waves and swells, 

 by tidal or other currents, and by the motion of ships, 

 fish, etc. These irregularities in velocity, although 

 small in comparison with the velocity of sound, may 

 easily cause appreciable alterations in the shape and 

 strength of an explosive pulse at ranges of the order 

 of a thousand yards. 



Unfortunately, the experimental data so far avail- 

 able are not sufficiently complete to enable many sure 

 conclusions to be drawn about the mechanisms re- 

 sponsible for the various effects observed. However, a 

 few tentative conclusions can be reached regarding 

 the origin of the sound which is found in the shadow 

 zone in experiments such as those of references 8 and 

 9 which have been discussed in the preceding section. 

 Referring to Figure 5, it will be seen that in the 



